Find the cartesian equation of a plane which passes through the point (3,-4,1) and is parallel to the plane containing the point (1,2,-1) and the liner=t(1,1,1).

The answer is 3x-2y-z=16. I don't know how to find the normal vector of the plane. I know that the fixed point is (3,-4,1). Please help.

I'm really weak in vectors, is there any way to improve my mastery of this topic?